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Photoemission spectroscopy of amorphous hydrogenated germanium
Journal of Non-Crystalline Solids 35 & 36. (1980) 453-458 ~North-Holland Publishing Company
PHOTOEMISSION SPECTROSCOPYOF AMORPHOUS HYDROGENATED GERMANIUM K.J. Gruntz, L. Ley, M. Cardona, R. Johnson, G. Harbeke, and B. yon Roedern Max-Planck-Institut fur FestkBrperforschung, 7000 Stuttgart 80, Federal Republic of Germany
A number of different bonding configurations of hydrogen in a-Ge are identified on the basis of photoemission spectra. Hybridization coefficients are deduced from cross section variations with photon energy. Doping of a-Ge:H is achieved and shifts in the Fermi level are measured. Photolysis and surface enrichment of hydrogen is observed for the f i r s t time. INTRODUCTION This is an extension of our earlier work on photoemission of a-Si: H (von Roedern et al. (1977),(1979)) to amorphous hydrogenated germanium (a-Ge:H). A detailed picture of the effect of hydrogen incorporation and doping on the electronic structure of a-Ge:H has been obtained. The energy dependence of the part i a l photoemission cross sections gives the H-Ge hybridization for t'~e strongest bands associated with the hydrogen. Surface enrichment of hydrogen takes place during annealing and hydrogen photolysis has been detected, we believe, for the f i r s t time. EXPERIMENTAL The a-Ge:H films were deposited by dc glow discharge inside the photoelectron spectrometer onto freshly sputtered Mo substrates acting as the cathode. Voltage and pressure were 500 V and 0.3 torr. The gas used was 10 % GeH~ in argon. A range of exciting radiation (h~(eV) = 16.8(Nel), 21.2(Hel), 26.9(NeII), 40.8 (Hell), 1486.6(AIK~)) was utilized in conjunction with a simple monochromator (not for AIt K~hE ) Fermi to measure level valence- and core-level spectra. All energies are referred to EF• HYDROGEN INDUCEDFEATURES IN THE VALENCE BANDSOF a-Ge:H Fig. 1 shows the Hel spectrum obtained for three films prepared with different flow rates of the GeHw-Ar gas. The leading, Ge 3p derived peak between EF and 4 eV is followed by prominent hydrogen induced features around 5 eV. All films contain Ar as shown by the presence of the 3p line at 9.15 eV (Waclawski et a1. (1978)). We distinguish two different bonding states of hydrogen in a-Ge. One gives rise to peak C at ~5.0 eVand the other to peak A at 5.8 eV. The film prepared with the intermediate flow rate contains apparently hydrogen in both configurations. At even higher concentrations of hydrogen the spectrum (Fig. 2) is dominated by the peak A and a third peak A' at 6.8 eV can be distinguished as well. A deep lying doublet BI and B2 at 11.1 eV and 12.1 eV, respectively, shows up in the Hell spectrum of Fig. 2. Asthis film is taken through a series of annealing step~ hydrogen is driven out i n i t i a l l y from the configurations corresponding to peaks A and A'. This is accompanied by a reduction of BI and B2 which shift at the same time to lower binding energies. At an annealing temperature TA = 220°C the f i r s t depletion step is completed and hydrogen remains only at sites associated with peak C and a now visible peak D at 7.3 eV. The separation C-D is 2.3 eV
453
45~
K.J. Gruntz et al. /Amorphous Hgdrogenated Germanium
I
I
a= Ge: H
I
•
I
c A
Ar
I
.~
in c ¢m 1
m c o
-
--
i
,
EF
I
I
I
"1
l
m
m
•
5
I
,,
,
tO
Binding energy (ev)
Figure 1 Valence band spectra of a-Ge:H (hv = 21.2 eV) of gd films prepared with different flow rates: 0.02 l/h ( - - ) , 0.04 l/h ( - - - ) , and 0.1 l/h ( . . . . ).
a-Ge:H ¥_l~
?/
I o-Ge:H B1 B2
Ull ,almB
C ,.J
m
190
190 220o(
c c
I 250°C
300 EF
5
10
EF
5
10
15
Binding Energy (eV) Figure 2 Hel and Hell photoemission spectra of a-Ge:H as a function of annealing temperature T A.
K.J. Gruntz et al. /Amorphous Hgdrogenated Germanium
~55
in a-Ge:H, slightly more than the corresponding 2.1 eV in a-Si:H (yon Roedern et al. (1979)). Hydrogen chemisorbes on Ge(100) as singl/ bonded GeH and the photoemission spectrum (Appelbaum et al. (1978)) shows two Drominent hydrogen induced levels at 4.8 eV and 7.5 eV. We therefore identify the~e two peaks with a monohydride configuration. This hydrogen species evolves for TA > 220oc and the film • • r= ~ I is hydrogen-free at_TA --- 400O C. Peaks A, A| and Bz, B2 are most l i •k e l y due to configurations involving more than one hydrogen atom attached to a Ge atom. The incorporation of hydrogen leads to a recess of the top of the valence bands EV o f ~ 0 . 3 eV and of about 0.7 eV at a point half way up it~ leading edge. With annealing E~ moves back towards EF as shown in Fig. 3. The shape of Ev - EF as a function of TA follows closely the crystallization curve measured b~ Bermejo et al. (1979). The binding energy of the Ge 3d core levels is also reduced but the position of the Ar 3p level remains unchanged. An explanation of these shifts in terms of a pinning of EF after crystallization due to surface states can therefore be excluded. The changes in EV - EF and in E(Ge 3d) must be due to the variation in hydrogen content, The Ge-H configuration (peaks C+D) appears to be more effective in removing st=t~s from the top of the valence bands than the Ge-Hn (n ~ 2) configurations. !
|
I
'13
Qm
eV
C
a-Ge:H
O.5 0.5
"
I
0
8 0.3
eb,
e
~eReDeieIO
= E V-EF
0.2 - oE (Ge3d5/2)-29.02 eV EF:O.
0
'
100
200
=~
=
'
300
=
2:
I'
/,00
TA (°C) Figure 3 Hydrogen content and shifts in the top of the valence bands (Ev) and the Ge 3d core level with annealing temperature TA.
SURFACE ENRICHMENTOF HYDROGEN The surface of a-Ge:H becomes enriched with hydrogen during the annealing procedure (see Fig. 4). Hence an excess iotensity of ~e hydrogen peaks is found in the HeII spectra where the sampl~g depth is only 5 A compared to the HeI spectra with a sampling depth of ~20/I(Ibach (1977)). The hydrogen is either trapped at the surface while i t diffuses out of the bulk because the surface is at a somewhat lower temperature while the film cools down or the desorption kinetics are slower at the surface compared to the bulk. THE CROSSSECTIONOF THE HYDROGENINDUCEDLEVELS The Ge and H partial photoionization cross sections vary rapidly between 1 0 ~ h~ < 40 eV. Following procedures detailed by Eastman and Freeouf (1975) and neglect i n g interference effects (Braun et al. 1974) we assume that the total emission
456
K.J. Gruntz et al. /Amorphous Hydrogenated Germanium
..jO
I
=:=:
I
".
,=o.sl-
~-
0
I
'%
0
100
4
=~.=~_
200
-i
300
L,O0
TA (=C) Figure 4 Normalized intensity of hydrogen induced peaks in HeI and Hel: spectra as a function annealing temperature. intensity !A(H) of ~he hydrogen p~aks at 52eV can be factorized into hv-independent hydrogen i~(a~) and Ge 4p ( ~ = 1 - aH) local densities of states and hv-dependent cross ~gctions oH(hv) ~nd op(hv). Thus IA(H,hv) = OH(bY) " a~ + Cp(hV) (l-a~) i f we take oH from the works of Samson eL al. (1965) and Inoue et al. (1979) and oD from Feuerbacher et al. (1968) together with photoemission data on c-Ge and u~e the appropriate asymmetry parameters for our geometry (Manson (1972/73)) we find (see Fig. 5) that the energy dependence of IA(H) is compatible with a 64 % contribution of Hls and 36 % Ge 4p states in the peak at ~5 eV binding energy. This result is in agreement with 60 % H l s contribution to the density of states calculated by Ching et a1, (1979) for the corresponding peak in a-Si:H with h2drogen in the Si-H3 configuration.
]A(H)
i
I
I
J.'co,,)l 18"
i 6[-
OH=0.8 experiment
~'"
NeI HeI~Ne 1I _~/t a''" ,
10
I"
a-Ge:H
20
.,
He. ,
30
hv (eV)
/,0
Figure 5 Area IA(H ) under the hydrogen peak normalized to the Ge 4p emission Ip(Ge). at 2,8 eV as a function of photon energy, Calculated and experimental values ?re normalized for the HeI spectrum,
K.J. Gruntz et al. /Amorphous Hydrogenated Germanium
457
DOPING OF a-Ge:H Films of a-Ge:H deposited at a substrate temperature Ts = 200°C could be doped w~th P and B by adding PH3 and B2H6 to the discharge gas. Fig. 5 shows the shift in EF as a function of dopant concentration. The concentration of doping atoms actually incorporated was determined for the highest concentration from the intensity of P-and B-core levels relative to those of Ge using the appropriate photoemission cross sections (Leckey (1976)).If each doping atom ~s electrically active we obtain from the shift in EF an average density of gap states of about 2x10 2° states/eV.
Ratio of dopant atoms incorporated B/Ge P/Ge I0"
10.2
10.3
10.3
10.2
10" 0
olO/-
1 E (Ge3dB/z)=2 O~
<3 -0.2"°1 f
=05e •
I
•
10"1
.
I
|0-2
.
.
I
•
.,,,,
..
10-3 "
.
I
,
•
10-3
10-2
I
,
|0 "1
B2H6 PH3 Concentrationin Ge H& Figure 6 Shift in EF as a function of doping. A EF is measured by the s h i f t of EF relative to the Ge 3d5/2 core level.
PHOTOINDUCED HYDROGEN DESORPTION IN a-Ge:H We observed for al~l films a pronounced reduction in the hydrogen peak after i r radiation with the unmonochronatized l i g h t from the discharge ]amp used to take the spectra. Ne radiation appears to be mor~ e f f i c i e n t in removing the hydrogen than He radiation (see Fin. 6). Since unmonochromatized l i g h t seems to remove hydrogen more readily t h ~ ~onochromatized l i g h t the low energy continuum (hv 10 eV) is most l i k e l y responsible for breakin~ the Ge-hydrogen bond. Photolysis of matrix isolated GeHL~,::~th l i g h t below 11 eV has been observed by Smith et al. (1972). A study of the spectral dependei;ce of the photolysis (synchrotron radiation?) in a-Ge:H should yield most valuable information. Conceivably i r r a d i a t i o n with a given wavelength could be used to remo~e undesirable forms of H-bonding and improve the e l e c t r i c a l properties of such films. Also, i t may be possible to scribe with uv i r r a d i a t i o n onto a-Si:H and/or a-Ge:H structures of potential value as Jevices. ACKNOWLEDGEMENT We are indebted to W. Neu and G. Krutina for their technical help and to C.C. Lin for information concerning the partial densities of states in a-Si:H.
~58
K.Jo Gruntz et al. / Amorphous Hgdrogenated Germanium
~.
1
,,.z~
Herodiotion
Ne rodiation
o~
ge I-
o.s
0
0
1
2 Time (hours)
3
Figure 7 Decrease in hydrogen concentration of a number of a-Ge:H films after irradiation with He and Ne radiation from a windowless discharge lamp. REFERENCES
Appelbaum J.A., Baraff G.A., HamannD.R., Hagstrum H.D., Sakurai T. (1978) Surf. Science 70, 654. Bermejo D., Car--6onaM. (1979), J. Non-Cryst. Sol. 32, 421. Braun W., GoldmannA., Cardona M. (1974), Phys. Re~ BIO, 5069. Ching W.Y., Lam D.J., Lin C.C. (1979), (private commutation). Eastman b.E., Freeouf J.L. (1975), Phys. Rev. Lett. 7, 395. Ibach H. (1977) in Electron Spectroscopy for Surface-Analycis, H Ibach editor (Springer, Berlin 1971), p . I . . . . . . "" " Inoue K., Kanzaki H., Suga S. (1979), Sol. State Comm. (to be published). Leckey R.C.G. (1976), Phys. Rev. A13, 1043. Manson S.T. (1972/3), J. Electr. ~-p-6ctrosc. 1, 413. Samson J.A.R., Cairns R.B. (1965), j . Opt. S~c. Am. 55, 1035. Smith G.R., Guillory W.A. (1972), J. Chem. Phys. 56,~423. von Roedern B., Ley L., Cardona M.(1977), Phys. R~. Lett. 39, 1576. von Roedern B., Ley L., Cardona M., Smith F.W. (1979), Phil.--Mag. (to be pubI i shed) Waclawski B.J., Gadzuk J.W., Herbst J.F. (1978), Phys. Rev. Lett. 4..11, 583.
PHOTOEMISSION SPECTROSCOPYOF AMORPHOUS HYDROGENATED GERMANIUM K.J. Gruntz, L. Ley, M. Cardona, R. Johnson, G. Harbeke, and B. yon Roedern Max-Planck-Institut fur FestkBrperforschung, 7000 Stuttgart 80, Federal Republic of Germany
A number of different bonding configurations of hydrogen in a-Ge are identified on the basis of photoemission spectra. Hybridization coefficients are deduced from cross section variations with photon energy. Doping of a-Ge:H is achieved and shifts in the Fermi level are measured. Photolysis and surface enrichment of hydrogen is observed for the f i r s t time. INTRODUCTION This is an extension of our earlier work on photoemission of a-Si: H (von Roedern et al. (1977),(1979)) to amorphous hydrogenated germanium (a-Ge:H). A detailed picture of the effect of hydrogen incorporation and doping on the electronic structure of a-Ge:H has been obtained. The energy dependence of the part i a l photoemission cross sections gives the H-Ge hybridization for t'~e strongest bands associated with the hydrogen. Surface enrichment of hydrogen takes place during annealing and hydrogen photolysis has been detected, we believe, for the f i r s t time. EXPERIMENTAL The a-Ge:H films were deposited by dc glow discharge inside the photoelectron spectrometer onto freshly sputtered Mo substrates acting as the cathode. Voltage and pressure were 500 V and 0.3 torr. The gas used was 10 % GeH~ in argon. A range of exciting radiation (h~(eV) = 16.8(Nel), 21.2(Hel), 26.9(NeII), 40.8 (Hell), 1486.6(AIK~)) was utilized in conjunction with a simple monochromator (not for AIt K~hE ) Fermi to measure level valence- and core-level spectra. All energies are referred to EF• HYDROGEN INDUCEDFEATURES IN THE VALENCE BANDSOF a-Ge:H Fig. 1 shows the Hel spectrum obtained for three films prepared with different flow rates of the GeHw-Ar gas. The leading, Ge 3p derived peak between EF and 4 eV is followed by prominent hydrogen induced features around 5 eV. All films contain Ar as shown by the presence of the 3p line at 9.15 eV (Waclawski et a1. (1978)). We distinguish two different bonding states of hydrogen in a-Ge. One gives rise to peak C at ~5.0 eVand the other to peak A at 5.8 eV. The film prepared with the intermediate flow rate contains apparently hydrogen in both configurations. At even higher concentrations of hydrogen the spectrum (Fig. 2) is dominated by the peak A and a third peak A' at 6.8 eV can be distinguished as well. A deep lying doublet BI and B2 at 11.1 eV and 12.1 eV, respectively, shows up in the Hell spectrum of Fig. 2. Asthis film is taken through a series of annealing step~ hydrogen is driven out i n i t i a l l y from the configurations corresponding to peaks A and A'. This is accompanied by a reduction of BI and B2 which shift at the same time to lower binding energies. At an annealing temperature TA = 220°C the f i r s t depletion step is completed and hydrogen remains only at sites associated with peak C and a now visible peak D at 7.3 eV. The separation C-D is 2.3 eV
453
45~
K.J. Gruntz et al. /Amorphous Hgdrogenated Germanium
I
I
a= Ge: H
I
•
I
c A
Ar
I
.~
in c ¢m 1
m c o
-
--
i
,
EF
I
I
I
"1
l
m
m
•
5
I
,,
,
tO
Binding energy (ev)
Figure 1 Valence band spectra of a-Ge:H (hv = 21.2 eV) of gd films prepared with different flow rates: 0.02 l/h ( - - ) , 0.04 l/h ( - - - ) , and 0.1 l/h ( . . . . ).
a-Ge:H ¥_l~
?/
I o-Ge:H B1 B2
Ull ,almB
C ,.J
m
190
190 220o(
c c
I 250°C
300 EF
5
10
EF
5
10
15
Binding Energy (eV) Figure 2 Hel and Hell photoemission spectra of a-Ge:H as a function of annealing temperature T A.
K.J. Gruntz et al. /Amorphous Hgdrogenated Germanium
~55
in a-Ge:H, slightly more than the corresponding 2.1 eV in a-Si:H (yon Roedern et al. (1979)). Hydrogen chemisorbes on Ge(100) as singl/ bonded GeH and the photoemission spectrum (Appelbaum et al. (1978)) shows two Drominent hydrogen induced levels at 4.8 eV and 7.5 eV. We therefore identify the~e two peaks with a monohydride configuration. This hydrogen species evolves for TA > 220oc and the film • • r= ~ I is hydrogen-free at_TA --- 400O C. Peaks A, A| and Bz, B2 are most l i •k e l y due to configurations involving more than one hydrogen atom attached to a Ge atom. The incorporation of hydrogen leads to a recess of the top of the valence bands EV o f ~ 0 . 3 eV and of about 0.7 eV at a point half way up it~ leading edge. With annealing E~ moves back towards EF as shown in Fig. 3. The shape of Ev - EF as a function of TA follows closely the crystallization curve measured b~ Bermejo et al. (1979). The binding energy of the Ge 3d core levels is also reduced but the position of the Ar 3p level remains unchanged. An explanation of these shifts in terms of a pinning of EF after crystallization due to surface states can therefore be excluded. The changes in EV - EF and in E(Ge 3d) must be due to the variation in hydrogen content, The Ge-H configuration (peaks C+D) appears to be more effective in removing st=t~s from the top of the valence bands than the Ge-Hn (n ~ 2) configurations. !
|
I
'13
Qm
eV
C
a-Ge:H
O.5 0.5
"
I
0
8 0.3
eb,
e
~eReDeieIO
= E V-EF
0.2 - oE (Ge3d5/2)-29.02 eV EF:O.
0
'
100
200
=~
=
'
300
=
2:
I'
/,00
TA (°C) Figure 3 Hydrogen content and shifts in the top of the valence bands (Ev) and the Ge 3d core level with annealing temperature TA.
SURFACE ENRICHMENTOF HYDROGEN The surface of a-Ge:H becomes enriched with hydrogen during the annealing procedure (see Fig. 4). Hence an excess iotensity of ~e hydrogen peaks is found in the HeII spectra where the sampl~g depth is only 5 A compared to the HeI spectra with a sampling depth of ~20/I(Ibach (1977)). The hydrogen is either trapped at the surface while i t diffuses out of the bulk because the surface is at a somewhat lower temperature while the film cools down or the desorption kinetics are slower at the surface compared to the bulk. THE CROSSSECTIONOF THE HYDROGENINDUCEDLEVELS The Ge and H partial photoionization cross sections vary rapidly between 1 0 ~ h~ < 40 eV. Following procedures detailed by Eastman and Freeouf (1975) and neglect i n g interference effects (Braun et al. 1974) we assume that the total emission
456
K.J. Gruntz et al. /Amorphous Hydrogenated Germanium
..jO
I
=:=:
I
".
,=o.sl-
~-
0
I
'%
0
100
4
=~.=~_
200
-i
300
L,O0
TA (=C) Figure 4 Normalized intensity of hydrogen induced peaks in HeI and Hel: spectra as a function annealing temperature. intensity !A(H) of ~he hydrogen p~aks at 52eV can be factorized into hv-independent hydrogen i~(a~) and Ge 4p ( ~ = 1 - aH) local densities of states and hv-dependent cross ~gctions oH(hv) ~nd op(hv). Thus IA(H,hv) = OH(bY) " a~ + Cp(hV) (l-a~) i f we take oH from the works of Samson eL al. (1965) and Inoue et al. (1979) and oD from Feuerbacher et al. (1968) together with photoemission data on c-Ge and u~e the appropriate asymmetry parameters for our geometry (Manson (1972/73)) we find (see Fig. 5) that the energy dependence of IA(H) is compatible with a 64 % contribution of Hls and 36 % Ge 4p states in the peak at ~5 eV binding energy. This result is in agreement with 60 % H l s contribution to the density of states calculated by Ching et a1, (1979) for the corresponding peak in a-Si:H with h2drogen in the Si-H3 configuration.
]A(H)
i
I
I
J.'co,,)l 18"
i 6[-
OH=0.8 experiment
~'"
NeI HeI~Ne 1I _~/t a''" ,
10
I"
a-Ge:H
20
.,
He. ,
30
hv (eV)
/,0
Figure 5 Area IA(H ) under the hydrogen peak normalized to the Ge 4p emission Ip(Ge). at 2,8 eV as a function of photon energy, Calculated and experimental values ?re normalized for the HeI spectrum,
K.J. Gruntz et al. /Amorphous Hydrogenated Germanium
457
DOPING OF a-Ge:H Films of a-Ge:H deposited at a substrate temperature Ts = 200°C could be doped w~th P and B by adding PH3 and B2H6 to the discharge gas. Fig. 5 shows the shift in EF as a function of dopant concentration. The concentration of doping atoms actually incorporated was determined for the highest concentration from the intensity of P-and B-core levels relative to those of Ge using the appropriate photoemission cross sections (Leckey (1976)).If each doping atom ~s electrically active we obtain from the shift in EF an average density of gap states of about 2x10 2° states/eV.
Ratio of dopant atoms incorporated B/Ge P/Ge I0"
10.2
10.3
10.3
10.2
10" 0
olO/-
1 E (Ge3dB/z)=2 O~
<3 -0.2"°1 f
=05e •
I
•
10"1
.
I
|0-2
.
.
I
•
.,,,,
..
10-3 "
.
I
,
•
10-3
10-2
I
,
|0 "1
B2H6 PH3 Concentrationin Ge H& Figure 6 Shift in EF as a function of doping. A EF is measured by the s h i f t of EF relative to the Ge 3d5/2 core level.
PHOTOINDUCED HYDROGEN DESORPTION IN a-Ge:H We observed for al~l films a pronounced reduction in the hydrogen peak after i r radiation with the unmonochronatized l i g h t from the discharge ]amp used to take the spectra. Ne radiation appears to be mor~ e f f i c i e n t in removing the hydrogen than He radiation (see Fin. 6). Since unmonochromatized l i g h t seems to remove hydrogen more readily t h ~ ~onochromatized l i g h t the low energy continuum (hv 10 eV) is most l i k e l y responsible for breakin~ the Ge-hydrogen bond. Photolysis of matrix isolated GeHL~,::~th l i g h t below 11 eV has been observed by Smith et al. (1972). A study of the spectral dependei;ce of the photolysis (synchrotron radiation?) in a-Ge:H should yield most valuable information. Conceivably i r r a d i a t i o n with a given wavelength could be used to remo~e undesirable forms of H-bonding and improve the e l e c t r i c a l properties of such films. Also, i t may be possible to scribe with uv i r r a d i a t i o n onto a-Si:H and/or a-Ge:H structures of potential value as Jevices. ACKNOWLEDGEMENT We are indebted to W. Neu and G. Krutina for their technical help and to C.C. Lin for information concerning the partial densities of states in a-Si:H.
~58
K.Jo Gruntz et al. / Amorphous Hgdrogenated Germanium
~.
1
,,.z~
Herodiotion
Ne rodiation
o~
ge I-
o.s
0
0
1
2 Time (hours)
3
Figure 7 Decrease in hydrogen concentration of a number of a-Ge:H films after irradiation with He and Ne radiation from a windowless discharge lamp. REFERENCES
Appelbaum J.A., Baraff G.A., HamannD.R., Hagstrum H.D., Sakurai T. (1978) Surf. Science 70, 654. Bermejo D., Car--6onaM. (1979), J. Non-Cryst. Sol. 32, 421. Braun W., GoldmannA., Cardona M. (1974), Phys. Re~ BIO, 5069. Ching W.Y., Lam D.J., Lin C.C. (1979), (private commutation). Eastman b.E., Freeouf J.L. (1975), Phys. Rev. Lett. 7, 395. Ibach H. (1977) in Electron Spectroscopy for Surface-Analycis, H Ibach editor (Springer, Berlin 1971), p . I . . . . . . "" " Inoue K., Kanzaki H., Suga S. (1979), Sol. State Comm. (to be published). Leckey R.C.G. (1976), Phys. Rev. A13, 1043. Manson S.T. (1972/3), J. Electr. ~-p-6ctrosc. 1, 413. Samson J.A.R., Cairns R.B. (1965), j . Opt. S~c. Am. 55, 1035. Smith G.R., Guillory W.A. (1972), J. Chem. Phys. 56,~423. von Roedern B., Ley L., Cardona M.(1977), Phys. R~. Lett. 39, 1576. von Roedern B., Ley L., Cardona M., Smith F.W. (1979), Phil.--Mag. (to be pubI i shed) Waclawski B.J., Gadzuk J.W., Herbst J.F. (1978), Phys. Rev. Lett. 4..11, 583.